If y ≠ 0, is y 0? (1) |y| 1 (2) y^2 + y/y^2 1

Question

If y ≠ 0, is y > 0?

(1)  |y| > 1

(2)  \frac{y^2 + y}{y^2} > 1

NiharikaR · Answer

IMO B

St1 y>1 or y<-1
insufficient

St2 y^2+y>y^2 (sq quantity is +ve)
y>0
sufficient

chetan2u · Answer

NiharikaR , ans should be B..
 
(1)  |y| > 1 
tells us that y<-1 or y>1
insuff

(2)  \frac{y^2 + y}{y^2} > 1 ..
 Cross multiply as y^2 is POSITIVE
 y^2 + y > y^2.............y>y^2-y^2.......y>0 ..
suff

B

NiharikaR · Answer

Thanks. I read the question wrong. I thought its asking y>1.
Though I got y>0, I wrote insufficient.

I have to avoid such silly mistakes during exam

AV24 · Answer

I ) |y| > 1

y>1
y <-1

not sufficient

II)
 y^2+y/y^2  > 1

y^2/y^2 + y/y^2 > 1

1 + 1/y >1 ==> 1/y >0 ==> y>0

sufficient

Therefore B

push12345 · Answer

I) y could be 2 or -2
Insufficient

II) rewriting eqn
1+(1/y)>1

1/y>0
Y>0

So b is ANS

Posted from my mobile device

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (y) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If  y = 1 , then  y > 0 . The answer is "yes".
If  y = -1 , then  y < 0 . The answer is "no".
Since we don't have a unique solution, the condition 1) is not sufficient.

Condition 2)

\frac{y^2 + y}{y^2} > 1 
 ⇔ y^2 + y > y^2 
 ⇔ y > 1 
Then we have  y > 0 .

Condition 2) is sufficient.

Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

merajul · Answer

If y ≠ 0, is y > 0?

(1)  |y| > 1

(2)  \frac{y^2 + y}{y^2} > 1

|y|>1 => y >1 or -y >1 => -1>y>1. Not Sufficient

(y^2+y) / y^2 >1
=> 1 + (1/y) >1
=> 1/y > 0
=> y > 0 SUFFICIENT

If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1

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